Question

tìm GTLN GTNN của :

y = sin2x +√3 cos²x +1

Answer 1

\(y=sin2x+\sqrt{3}\left(\frac{1+cos2x}{2}\right)+1\)

\(=sin2x+\frac{\sqrt{3}}{2}cos2x+1+\frac{\sqrt{3}}{2}\)

\(=\frac{\sqrt{7}}{2}\left(sin2x.\frac{2\sqrt{7}}{7}+\frac{\sqrt{21}}{7}cos2x\right)+1+\frac{\sqrt{3}}{2}\)

\(=\frac{\sqrt{7}}{2}.sin\left(2x+a\right)+1+\frac{\sqrt{3}}{2}\)

(Với \(cosa=\frac{2\sqrt{7}}{7};sina=\frac{\sqrt{21}}{7}\))

\(\Rightarrow-\frac{\sqrt{7}}{2}+1+\frac{\sqrt{3}}{2}\le y\le\frac{\sqrt{7}}{2}+1+\frac{\sqrt{3}}{2}\)